Materials Science and Engineering. An Introduction

William D. Callister

Chapter 10

Phase Transformations in Metals: Development of Microstructure and Alteration of Mechanical Properties - all with Video Answers

Educators

Chapter Questions

Problem 1

Name the two stages involved in the formation of particles of a new phase. Briefly describe each.

Hunza Gilgit

Hunza Gilgit

Numerade Educator

Problem 2

(a) Rewrite the expression for the total free energy change for nucleation (Equation 10.1) for the case of a cubic nucleus of edge length $a$ (instead of a sphere of radius $r$ ). Now differentiate this expression with respect to $a$ (per Equation 10.2) and solve for both the critical cube edge length, $a^*$, and also $\Delta G^*$.
(b) Is $\Delta G^*$ greater for a cube or a sphere? Why?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 3

If ice homogeneously nucleates at $-40^{\circ} \mathrm{C}$, calculate the critical radius given values of $-3.1 \times 10^8 \mathrm{~J} / \mathrm{m}^3$ and $25 \times 10^{-3} \mathrm{~J} / \mathrm{m}^2$, respectively, for the latent heat of fusion and the surface free energy.

Manik Pulyani

Numerade Educator

Problem 4

(a) For the solidification of nickel, calculate the critical radius $r^*$ and the activation free energy $\Delta G^*$ if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are $-2.53 \times 10^9 \mathrm{~J} / \mathrm{m}^3$ and $0.255 \mathrm{~J} / \mathrm{m}^2$, respectively. Use the supercooling value found in Table 10.1.
(b) Now calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.360 nm for solid nickel at its melting temperature.

Manik Pulyani

Numerade Educator

Problem 5

(a) Assume for the solidification of nickel (Problem 10.4) that nucleation is homogeneous, and the number of stable nuclei is $10^6$ nuclei per cubic meter. Calculate the critical radius and the number of stable nuclei that exist at the following degrees of supercooling: 200 K and 300 K .
(b) What is significant about the magnitudes of these critical radii and the numbers of stable nuclei?

Manik Pulyani

Numerade Educator

Problem 6

For some transformation having kinetics that obey the Avrami equation (Equation 10.17), the parameter $n$ is known to have a value of 1.5 . If, after 125 s , the reaction is $25 \%$ complete, how long (total time) will it take the transformation to go to $90 \%$ completion?

Manik Pulyani

Numerade Educator

Problem 7

Compute the rate of some reaction that obeys Avrami kinetics, assuming that the constants $n$ and $k$ have values of 2.0 and $5 \times 10^{-4}$, respectively, for time expressed in seconds.

Manik Pulyani

Numerade Educator

Problem 8

It is known that the kinetics of recrystallization for some alloy obey the Avrami equation, and that the value of $n$ in the exponential is 5.0 . If, at some temperature, the fraction recrystallized is 0.30 after 100 min , determine the rate of recrystallization at this temperature.

Manik Pulyani

Numerade Educator

Problem 9

The kinetics of the austenite-to-pearlite transformation obey the Avrami relationship.
Using the fraction transformed-time data given here, determine the total time required for $95 \%$ of the austenite to transform to pearlite:
$$
\begin{array}{cc}
\hline \text { Fraction Transformed } & \text { Time }(\boldsymbol{s}) \\
\hline 0.2 & 280 \\
0.6 & 425 \\
\hline
\end{array}
$$

Manik Pulyani

Numerade Educator

Problem 10

The fraction recrystallized-time data for the recrystallization at $350^{\circ} \mathrm{C}$ of a previously deformed aluminum are tabulated here. Assuming that the kinetics of this process obey the Avrami relationship, determine the fraction recrystallized after a total time of 116.8 min .
$$
\begin{array}{cc}
\hline \text { Fraction Recrystallized } & \text { Time }(\text { min }) \\
\hline 0.30 & 95.2 \\
0.80 & 126.6 \\
\hline
\end{array}
$$

Manik Pulyani

Numerade Educator

Problem 11

(a) From the curves shown in Figure 10.11 and using Equation 10.18, determine the rate of recrystallization for pure copper at the several temperatures.
(b) Make a plot of $\ln ($ rate ) versus the reciprocal of temperature (in $\mathrm{K}^{-1}$ ), and determine the activation energy for this recrystallization process. (See Section 5.5.)
(c) By extrapolation, estimate the length of time required for $50 \%$ recrystallization at room temperature, $20^{\circ} \mathrm{C}(293 \mathrm{~K})$.

Manik Pulyani

Numerade Educator

Problem 12

Determine values for the constants $n$ and $k$ (Equation 10.17) for the recrystallization of copper (Figure 10.11) at $119^{\circ} \mathrm{C}$.

Manik Pulyani

Numerade Educator

Problem 13

In terms of heat treatment and the development of microstructure, what are two major limitations of the iron-iron carbide phase diagram?

Hunza Gilgit

Numerade Educator

Problem 14

(a) Briefly describe the phenomena of superheating and supercooling.
(b) Why do these phenomena occur?

Hunza Gilgit

Numerade Educator

Problem 15

Suppose that a steel of eutectoid composition is cooled to $675^{\circ} \mathrm{C}\left(1250^{\circ} \mathrm{F}\right)$ from $760^{\circ} \mathrm{C}$ $\left(1400^{\circ} \mathrm{F}\right)$ in less than 0.5 s and held at this temperature.
(a) How long will it take for the austeniteto-pearlite reaction to go to $50 \%$ completion? To $100 \%$ completion?
(b) Estimate the hardness of the alloy that has completely transformed to pearlite.

Manik Pulyani

Numerade Educator

Problem 16

Briefly cite the differences between pearlite, bainite, and spheroidite relative to microstructure and mechanical properties.

Hunza Gilgit

Numerade Educator

Problem 17

What is the driving force for the formation of spheroidite?

Hunza Gilgit

Numerade Educator

Problem 18

Using the isothermal transformation diagram for an iron-carbon alloy of eutectoid composition (Figure 10.22), specify the nature of the final microstructure (in terms of microconstituents present and approximate percentages of each) of a small specimen that has been subjected to the following time-temperature treatments. In each case assume that the specimen begins at $760^{\circ} \mathrm{C}$ $\left(1400^{\circ} \mathrm{F}\right)$ and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure.
(a) Cool rapidly to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for $10^3 \mathrm{~s}$, then quench to room temperature.
(b) Rapidly cool to $625^{\circ} \mathrm{C}\left(1160^{\circ} \mathrm{F}\right)$, hold for 10 s , then quench to room temperature.
(c) Rapidly cool to $600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)$, hold for 4 s , rapidly cool to $450^{\circ} \mathrm{C}\left(840^{\circ} \mathrm{F}\right)$, hold for 10 s , then quench to room temperature.
(d) Reheat the specimen in part (c) to $700^{\circ} \mathrm{C}$ $\left(1290^{\circ} \mathrm{F}\right)$ for 20 h .
(e) Rapidly cool to $300^{\circ} \mathrm{C}\left(570^{\circ} \mathrm{F}\right)$, hold for 20 s , then quench to room temperature in water. Reheat to $425^{\circ} \mathrm{C}\left(800^{\circ} \mathrm{F}\right)$ for $10^3 \mathrm{~s}$ and slowly cool to room temperature.
(f) Cool rapidly to $665^{\circ} \mathrm{C}\left(1230^{\circ} \mathrm{F}\right)$, hold for $10^3 \mathrm{~s}$, then quench to room temperature.
(g) Rapidly cool to $575^{\circ} \mathrm{C}\left(1065^{\circ} \mathrm{F}\right)$, hold for 20 s , rapidly cool to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for 100 s , then quench to room temperature.
(h) Rapidly cool to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for 150 s , then quench to room temperature.

Manik Pulyani

Numerade Educator

Problem 19

Make a copy of the isothermal transformation diagram for an iron-carbon alloy of eutectoid composition (Figure 10.22) and then sketch and label time-temperature paths on this diagram to produce the following microstructures:
(a) $100 \%$ coarse pearlite
(b) $50 \%$ martensite and $50 \%$ austenite
(c) $50 \%$ coarse pearlite, $25 \%$ bainite, and $25 \%$ martensite

Manik Pulyani

Numerade Educator

Problem 20

Using the isothermal transformation diagram for a $1.13 \mathrm{wt} \%$ C steel alloy (Figure 10.39), determine the final microstructure (in terms of just the microconstituents present) of a small specimen that has been subjected to the following time-temperature treatments. In each case assume that the specimen begins at $920^{\circ} \mathrm{C}$ $\left(1690^{\circ} \mathrm{F}\right)$ and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure.
(a) Rapidly cool to $250^{\circ} \mathrm{C}\left(480^{\circ} \mathrm{F}\right)$, hold for $10^3 \mathrm{~s}$, then quench to room temperature.
(b) Rapidly cool to $775^{\circ} \mathrm{C}\left(1430^{\circ} \mathrm{F}\right)$, hold for 500 s , then quench to room temperature.
(c) Rapidly cool to $400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)$, hold for 500 s , then quench to room temperature.
(d) Rapidly cool to $700^{\circ} \mathrm{C}\left(1290^{\circ} \mathrm{F}\right)$, hold at this temperature for $10^5 \mathrm{~s}$, then quench to room temperature.
(FIGURE CAN'T COPY)
(e) Rapidly cool to $650^{\circ} \mathrm{C}\left(1200^{\circ} \mathrm{F}\right)$, hold at this temperature for 3 s , rapidly cool to $400^{\circ} \mathrm{C}$ $\left(750^{\circ} \mathrm{F}\right)$, hold for 25 s , then quench to room temperature.
(f) Rapidly cool to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for 300 s , then quench to room temperature.
(g) Rapidly cool to $675^{\circ} \mathrm{C}\left(1250^{\circ} \mathrm{F}\right)$, hold for 7 s , then quench to room temperature.
(h) Rapidly cool to $600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)$, hold at this temperature for 7 s , rapidly cool to $450^{\circ} \mathrm{C}$ $\left(840^{\circ} \mathrm{F}\right)$, hold at this temperature for 4 s , then quench to room temperature.

Manik Pulyani

Numerade Educator

Problem 21

For parts a, c, d, f, and h of Problem 10.20, determine the approximate percentages of the microconstituents that form.

Manik Pulyani

Numerade Educator

Problem 22

Make a copy of the isothermal transformation diagram for a $1.13 \mathrm{wt} \% \mathrm{C}$ iron-carbon alloy (Figure 10.39), and then on this diagram sketch and label time-temperature paths to produce the following microstructures:
(a) $6.2 \%$ proeutectoid cementite and $93.8 \%$ coarse pearlite
(b) $50 \%$ fine pearlite and $50 \%$ bainite
(c) $100 \%$ martensite
(d) $100 \%$ tempered martensite
(FIGURE CAN'T COPY)

Manik Pulyani

Numerade Educator

Problem 23

Name the microstructural products of eutectoid iron-carbon alloy $(0.76 \mathrm{wt} \% \mathrm{C})$ specimens that are first completely transformed to austenite, then cooled to room temperature at the following rates: (a) $1^{\circ} \mathrm{C} / \mathrm{s}$, (b) $20^{\circ} \mathrm{C} / \mathrm{s}$, (c) $50^{\circ} \mathrm{C} / \mathrm{s}$, and (d) $175^{\circ} \mathrm{C} / \mathrm{s}$.

Hunza Gilgit

Numerade Educator

Problem 24

Figure 10.40 shows the continuous cooling transformation diagram for a $0.35 \mathrm{wt} \%$ C iron-carbon alloy. Make a copy of this figure and then sketch and label continuous cooling curves to yield the following microstructures:
(a) Fine pearlite and proeutectoid ferrite
(b) Martensite
(c) Martensite and proeutectoid ferrite
(d) Coarse pearlite and proeutectoid ferrite
(e) Martensite, fine pearlite, and proeutectoid ferrite

Manik Pulyani

Numerade Educator

Problem 25

Cite two important differences between continuous cooling transformation diagrams for plain carbon and alloy steels.

Hunza Gilgit

Numerade Educator

Problem 26

Briefly explain why there is no bainite transformation region on the continuous cooling
(FIGURE CAN'T COPY)
transformation diagram for an iron-carbon alloy of eutectoid composition.

Manik Pulyani

Numerade Educator

Problem 27

Name the microstructural products of 4340 alloy steel specimens that are first completely transformed to austenite, then cooled to room temperature at the following rates:
(a) $0.005^{\circ} \mathrm{C} / \mathrm{s}$, (b) $0.05^{\circ} \mathrm{C} / \mathrm{s}$, (c) $0.5^{\circ} \mathrm{C} / \mathrm{s}$, and
(d) $5^{\circ} \mathrm{C} / \mathrm{s}$

Hunza Gilgit

Numerade Educator

Problem 28

Briefly describe the simplest continuous cooling heat treatment procedure that would be used in converting a 4340 steel from one microstructure to another.
(a) (Martensite + ferrite + bainite) to (martensite + ferrite + pearlite + bainite)
(b) (Martensite + ferrite + bainite) to spheroidite
(c) (Martensite + bainite + ferrite) to tempered martensite

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 29

On the basis of diffusion considerations, explain why fine pearlite forms for the moderate cooling of austenite through the eutectoid temperature, whereas coarse pearlite is the product for relatively slow cooling rates.
(FIGURE CAN'T COPY)

Hunza Gilgit

Numerade Educator

Problem 30

Briefly explain why fine pearlite is harder and stronger than coarse pearlite, which in turn is harder and stronger than spheroidite.

Jerrah Biggerstaff

Jerrah Biggerstaff

Numerade Educator

Problem 31

Cite two reasons why martensite is so hard and brittle.

Hunza Gilgit

Numerade Educator

Problem 32

Rank the following iron-carbon alloys and associated microstructures from the hardest to the softest: (a) $0.25 \mathrm{wt} \% \mathrm{C}$ with coarse pearlite, (b) $0.80 \mathrm{wt} \% \mathrm{C}$ with spheroidite, (c) $0.25 \mathrm{wt} \% \mathrm{C}$ with spheroidite, and (d) 0.80 $\mathrm{wt} \% \mathrm{C}$ with fine pearlite. Justify this ranking.

Manik Pulyani

Numerade Educator

Problem 33

Briefly explain why the hardness of tempered martensite diminishes with tempering time (at constant temperature) and with increasing temperature (at constant tempering time).

Hunza Gilgit

Numerade Educator

Problem 34

Briefly describe the simplest heat treatment procedure that would be used in converting a $0.76 \mathrm{wt} \% \mathrm{C}$ steel from one microstructure to the other, as follows:
(a) Martensite to spheroidite
(b) Spheroidite to martensite
(c) Bainite to pearlite
(d) Pearlite to bainite
(e) Spheroidite to pearlite
(f) Pearlite to spheroidite
(g) Tempered martensite to martensite
(h) Bainite to spheroidite

Manik Pulyani

Numerade Educator

Problem 35

(a) Briefly describe the microstructural difference between spheroidite and tempered martensite.
(b) Explain why tempered martensite is much harder and stronger.

Hunza Gilgit

Numerade Educator

Problem 36

Estimate the Rockwell hardnesses for specimens of an iron-carbon alloy of eutectoid composition that have been subjected to the heat treatments described in parts (d), (e), (f), (g), and (h) of Problem 10.18.

Manik Pulyani

Numerade Educator

Problem 37

Estimate the Brinell hardnesses for specimens of a $1.13 \mathrm{wt} \% \mathrm{C}$ iron-carbon alloy that have been subjected to the heat treatments described in parts (a), (d), and (h) of Problem 10.20 .

Manik Pulyani

Numerade Educator

Problem 38

Determine the approximate tensile strengths for specimens of a eutectoid iron-carbon alloy that have experienced the heat treatments described in parts (a), (b), and (d) of Problem 10.23.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 39

For a eutectoid steel, describe isothermal heat treatments that would be required to yield specimens having the following Brinell hardnesses: (a) 180 HB , (b) 220 HB , and (c) 500 HB .

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